Well only you really know what drives you. But when in your reply you say something like this I really wonder!
We can't inflate a balloon, cool it to room temperature, remove the balloon, and be left with a collection of compressed air.
You obviously don't like what I am saying and how the evidence has been supporting my argument, I think you then try and introduce some really odd "red herring" stuff to throw the conversation along a weird path.
It's not a red-herring. It's an accurate restatement of what you were proposing here:
It goes somthing like this.
Compress air in a bike pump the air will heat up, for you have done work compressing it, cool the bike pump and the air inside the pump and release the pressure on the plunger. The plunger won't return to the starting point till the expanding air is reheated.
And if you can't see it - consider a frictionless bike pump.
What's the difference between having a wall that presents no resitance, and having no wall?
Is none.
What's more, if you understood what I actually said instead of this knee jerk "Stop picking on me" sobbing, you would realize the answer is right in front of you.
In
both cases what would actually happen is that as soon as the confining pressure is released the gas, whether it be in the balloon, or the bike pump, the gas would expand and cool.
I can even tell you
why this happens.
Pressure is measured in terms of unit force per unit area.
When I apply a force to a body of gas, whether it be compressing it in a bike pump, or inflating a balloon, I am applying a force that opposes the force applied by the pressure, and the volume will be reduced until the force applied by the pressure is equal to the constraining force (either your hand, or the elastic force provided by the balloon).
If you cool the compressed volume back to its original temperature, then the same force is still going to be there.
The
only way to get around this is to cool it to well below its original temperature, and is probably going to involve a phase change, which has the result of reducing N. The point being, that the only way that your scenario has any validity is if you can cool it sufficiently to reduce P, because as long as a pressure differential exists, newtons laws of motion predict that expansion
must occur. But if you do that, then all you have is a cold gas with its pressure in equilibrium with its surroundings. But, you can achieve the same result by simply cooling the gas at a constant pressure.